Device for predicting values of a fluctuating system at a predetermined future time



MalCh 16, 1965 w` H. NEwx-:LL ETAL 3,174,030

DEVICE: FOR PREDICTING VALUES oF A FLUCTUATING SYSTEM AT A PREDETERMNED FUTURE TIME Original Filed May 29, 1953 l5 Sheets-Sheet 1 T( 4wd STAL ELEMENT ANR ANP.

ANP.

@Y @MW- A rrd/@v5 Y TEM March 16, 1965 w. H. NEWELL ETAL DEVICE FOR PREDICTING VALUES 0F A FLUCTUATING SYS AT A PREDETERMINED FUTURE TIME Original -Filed May 29, 1953 l5 Sheets-Sheet 2 .MSS

s 5 M NVAG r BZ w r Har@ A MDM/ aan@ MMM. www. m/ Y B March 16, 1965 w. H. NEWELI. ETAL 3,174,030

DEVICE FOR PREDICTING VALUES OF A FLUCTUATING SYSTEM AT A P-REDETERMINED FUTURE TIME Original Filed May 29, 1953 l5 Sheets-Sheet /IV VEN 70195 MECHA/v/snf (MfcffAn//CAL A 770,96-Y

March 16, 1965 w H NEWELL ETAL 3,174,030

DEVICE FOR PREDITING VALUES OF A FLUCTUATING SYSTEM AT A PREDETERMINED FUTURE TIME Original Filed May 29, 1953 15 Sheets-Sheet 4 477 47.5' 2 2 wf W2 Z To ,0% sro/ewa AN@ www/v6 I I 5 5/05': 1 500 I @MM- $02 1 T L' l -...J t l Il' lf3-Maron `50/)4' i ro /zvffGfA rae @1Q/V55 0F 503 l l 1' l March 16, 1965 w. H. NEWELL ETAL 3,174,030

DEVICE FOR PREDICTING VALUES OF A FLUCTUATING SYSTEM AT A PREDETERMINED FUTURE TIME Original Filed May 29, 1953 15 Sheets-Sheet 5 2 o 4 4 5 0 M 5 M W P 0 2 4 Q r. f m .mllll w 5 Av 6 .Mv Rnw 3 nw. D' L... M I

5 e M p. p.. 3 M M wl A K V. m mv .l M vlv M f l W f .Iv W. u v A' 7 uw N um om# 4 R .C R y p. x p A Mm 5 Y1 l. M M M M o .W 4 .l 7 .u un 7 v /m w. z/.m T2@ w/m^.i% m 5 5 M 5 .W J O M J P W J r. .l A r l \f I\ f` MV ra 1\ e p p. p. p. 6 2/ M a s M M M M A M M n MW w 5 w 5 5 M 5 5 a n s w 2e se W 0. OI p 5 25 M MMM? M MM M ,Mf

a www@ 3 EMM 5 March 15, 1965 w. H. NEwl-:LL ETAL 3,174,030

DEVICE FOR PREDICTING VALUES 0F A FLUCTUATING SYSTEM AT A PREDETERWNED FUTURE TIME original Filed May 2e, 195s 15 sheets-sheet e 527 ,4A/a 54156/- F/. 6.

S OF A FLUCTUATING SYSTEM AT A PREDETERMINED FUTURE TIME Original Filed May 29, 1953 March 16, 1965 w. H. NEWELL ETAL DEVICE EOE PEEDICTING VALUE 15 Sheets-Sheet '7 p Y VO TAGE mssl E w m w ATTORNEY March 16, 1965 3, DEVICE FOR PREDICTING VALUES OF A FLUCTUATING SYSTEM Original Filed May 29, 1953 w H.NEWE1 1 ETAL 174,030

AT A PREDETERMINED FUTURE TIME 15 Sheeis-Sheet 8 ATTORNEY March 16, 1965 w. H. NEWELI. ETAL 3,174,030

DEVICE FOR PREDICTING VALUES OF A FLUCTUATING SYSTEM AT A PREDETERMINED FUTURE TIME: Original Filed May 29, 1953 l5 Sheets-Sheet 9 March 16, 1965 W, NEWELL ETAL 3,174,030

DEVICE FOR PREDICTING VALUES OF A FLUCTUATING SYSTEM AT A PREDETERMINED FUTURE TIME Original Filed May 29, 1953 l5 Sheets-Sheet 10 March 16, 1965 w. H. NEWELL ETAL 3,174,030

DEVICE FOR PREDICTING VALUES 0F A FLUCTUATING SYSTEM AT A PBEDETERMINED FUTURE TIME Original Filed May 29, 1953 15 Sheets-Sheet 11 /Nvf/VTORS M//LL/AM H. /VfwELL fion/Afa 6.5MQGE5S /l/o/QMAA/f 2,455

DEVICE FOR PREDICTING VALUES 0F A FLUCTUATING SYSTEM AT A PREDE'IEJRMINED FUTURE TIME Original Filed May 29, 1953 l5 Sheets-Sheet. 12

msm

March 16, 1965 w. H. NEWELI. ETAL 3,174,030

DEVICE FOR PREDICTING VALUES OF A FLUCTUATING SYSTEM AT A PREDETERMINED FUTURE TIME Original Filed May 29, 1955 15 Sheets-Sheet 13 March 16, 1965 w` H. NEWELL ETAL 3,174,030

DEVICE EOE PREDICTING VALUES 0E A FLUCTUATING SYSTEM AT A PREDETERMINED FUTURE TIME Original Filed May 29, 1953 15 Sheets-Sheet 14 l-IA IVI/ENTORS E N .V

www: L

.SIA/14471152. FRAA/Gou/S BY MJ ArraR/v/EY March 16, 1965 w. H. NEwl-:LL ETAL 3,174,030

DEVICE FOR PREDICTING VALUES OF A-FLUCTUATING SYSTEM AT A PREDETERMINED FUTURE TIME /NVE/vrons MLU/1M f7. A/fwfLL Fon/,4,90 G. vease-55 /VofeMA/v f. ZAB@ 57AM/:ris Z FPA/V60U/$ A 7.70/9/VEY nited States Patent O 3,174,630 DEVICE FOR PREDICTING VALUES OF A FLUG- 'IUATING SYSTEM AT A PREDETEFMINED FU- TUBE 'HNE William H. Newell, Mount Vernon, Edward G. Burgess, lr., Kew Gardens, Norman l'. Zabb, Brooklyn, and Stamates l. Frangoulis, Flushing, NY., assignors to Sperry Rand Corporation, a corporation of Delaware Original application May 29, 1953, Ser. No. ,324, now Patent No. 2,996,706. Divided and this application May 26, 1955, Ser. No. SILlSZ 12 Claims. (Cl. 235-1S) The present application is a division of :application Serial No. 358,324 led May 29, i953, and now US. Patent No. 2,996,796.

rl`he present invention relates to a method and apparatus for computing the characteristics of ia iiuctuating system for a predetermined future period and for predieting the value of a quantity at the end of said period, even though the mathematical form of said system is varying, and although, the invention has a Wide range of utility, it is particularly useful in predicting the pitch angle (deck tilt) and the heave (deck level) of a floating platform, such as the flight deck of a carrier, at a future predetermined time.

In guiding an airplane in its approach towards a iioating platform, such as the deck 'of a carrier for landing, it is necessary to predict the future time of landing and the pitch angle and heave or level of the deck at the predicted time, to assure safe landing. Since the carrier is continuously oscillating in pitch and has a continuous oscillating vert-ical movement during the approach of the airplane, it becomes necessary to compute continuously the characterics of the iuctuating motions of the carrier and to predict therefrom the pitch and heave of the carrier at the future predicted time of landing. Since the movement of the deck does not follow a uniform mathematical pattern or equation, it is seen that the matter of determining with accuracy the pitch and heave at a future time is not a simple problem.

One object of the present invention is to provide a novel method and device by which the value of a quantity at a predetermined future time in a fluctuating system may be predicted, even though the mathematical form of the system may be continuously varying and the variations in the system may not be following a definite mathematical formula.

Another obiect is to lprovide a novel method and device by which the future pitch angle of a lloating platform, such as the flight deck of a carrier, at the predicted future instant of landing can be computed and predicted.

A further object is to provide a novel method and device by which the future heave or flight deck level of a floating platform, such as that of a carrier at the predicted future instant of landing can be computed and predicted.

ln accordance with the features of the present invention, the value of a quantity in a fluctuating system at a future predetermined time is predicted by following a cycle of operation including the steps of determining the present value of the quantity, deriving the futur characteristics of said system from said present value and predicting from the future characteristics of said system so derived the value of the fluctuating system for said predetermined time, and repeating said cycle of operation again and again up to the predetermined time but with the present values of the quantity revised for each cycle according to their true magnitudes, to obtain a succession of predicted values of the quantity for said predetermined time. ln accordance with the more specic aspects of the present invention, the succession of predicte ice values is obtained by a mechanizing operation as successive physical quantities and these physical quantities are smoothed as they are obtained, to merge them into' a substantially predicted quantity running from the end of the first cycle to near said predetermined time and increasing in accuracy as said predetermined time is appreached.

The general features of the present invention described are applied to the determination of the pitch angle and level of a lloating deck, such as the ilight deck of an aircraft carrier, at a future predetermined time, by employing the present values of the pitch angle and level in each cycle of the oscillating system, to determine the future characteristics of the pitch angle and level tluctuating systems and to determine therefrom the values of pitch angle and level for said predetermined time. B'y repeating these cycles up to the future predetermined time but with present values of the pitch angle and level brought up to date, and by smoothing the successive physical quantities representing the future values of pitch angle and deck level and obtained by mechanization, a continuous quantity is obtained, representing the future values of the pitch angle and deck, this continuous quantity becoming more accurate as said future predetermined time is approached.

Various other objects, features :and `advantages of the present invention are apparent from the following discription and from the accompanying drawings, in which FIG. l is a diagram of a rate measuring device oil the mechanical type to be used as part of an oscillating system for determining in accordance with the more specific aspects of the invention, the predicted pitch angle and predict-ed decl: level (heave) of a floating deck at a predicted future instant, the solid lines in said diagram indicating mechanical movements such as shaft rotations;

FIG. 2 is a diagram of a rate measuring device of the electrical type to be used as part of the oscillating system, the solid lines in said diagram representing electric signals and specifically voltages proportional to the values `of the quantities indicated on said diagram;

PEG. 3 is a diagram of an angular velocity function computer to be used as part of the oscillating system, the solid lines in said diagram indicating electric signals and specifically voltages and the dotted lines indicating shaft displacements;

FIG. 4 is a diagram of a mechanical oscillating prediction mechanism adapted to employ the values obtained from the rate measuring device of FlG. 1 and the angular velocity function computer of FIG. 3, to determine in accordance with the more specific aspects of the invention, the predicted pitch angle and predicted deck level (heave) of a floating deck at a predicted future linstant, the solid lines in said diagram indicating mechanical displacements and more specifically shaft rotations;

FlG. 5 is a diagram of a timing and control device for the oscillating prediction mechanism of FIG. 4, by which the different cycles and phases of operation are initiated and terminated at the proper time, the solid lines in said diagram indicating mechanical movements and the dotted lines electric impulses;

FIG. 6 is a diagram of an electrical oscillating prediction mechanism adapted to employ the values obtained from the rate measuring device of FIG. 2 and the angular velocity computer of FlG. 3, to determine in accordance with the more speciiic aspects of the invention, the predicted pitch angle and predicted deck level (heave) of a floating deck at a predicted future instant, the solid lines in said diagram indicating electric impulses and the dotted lines indicating mechanical displacements and more specifically shaft rotations;

PEG. 7 shows a form of electronic switch adapted to i.) be employed as part of the oscillating prediction mechanism of FIG. 6;

FIG. 8 `shows another form of electronic switch adapted to be employed as part of the oscillating prediction mechanism of FIG. 6;

FIG. 9 is a circuit diagram of a multivibrator and trigger device adapted to be employed as part of the oscillating prediction mechanism of FIG. 6 to control the timing and sequencing fof the different phases of the cycle of operation of said mechanism;

FIG. 10 is a chart indicating the diierent cycles of operation of the oscillating prediction mechanism of FIG. 6 and the corresponding voltage wave and pulse characteristics emanating from diierent parts of the multivibrator .and of the trigger circuit shown in FIG. 9;

FIG. 11 lshows diagrammatically one manner in which the principal devices of the oscillating system shown in FIGS. 1, 3, 4, 5 and 6 may be assembled to predict the value of a varying quantity at a predetermined time instant;

FIG. 12 shows diagram-matically the manner in which the principal devices of the oscillating system shown in FIGS. 3, 4, 5 and 6 may be assembled in conjunction with the modified form of rate measuring device shown in FIG. 13 to predict the value of a varying quantity at a predicted time instant;

FIG. 13 is a diagram of a modified form of rate measuring device adapted to be employed as part of the oscillating system of FIG. 12;

FIG. 14 shows diagrammaticallly the general assembly of a modified form of oscillating prediction system in which the rate measuring device and the oscillating prediction mechanism are combined to permit part of the rate measuring circuit to be employed as part of the oscillating prediction circuit;

FIGS. 15 and 16 when combined alo-ng the dot and dash Ibreak lines A show the oscillating prediction system of FIG. 14 in greater detail, the solid lines Iindicating electric impulses or signals, the dotted lines indicating mechanical displacements such as shaft rotations; and

FIG. 17 is a diagram of the oscillating prediction circuit of the oscillating prediction system of FIGS. 15 and 16 isolated from certain parts of the rate measuring device of said oscillating system, the solid lines indicating electric impulses 'or signals, the dotted lines indicating displacements, such `as shaft rotations.

To predict the position of a ships deck at the future instant yof landing of an approaching plane, it is required that the time ahead when the plane is expected to land be predicted and then that the position of the deck at this time be predicted. This sequence of predictions is based on the assumption that the pilot has sole control of the plane speed and that the position of the deck at touchdown (the posit-ion of the deck where the plane can begin to land) is not preselected.

The time required by 'a plane to fly from its present position to its position at touchdown on the deck indicated herein by the symbol Tp can be calculated by prediction time computer in the manner described in the aforesaid copending application. For computing the predicted pitch angle of the deck at the predicted time Tp of landing indicated by the symbol, it is necessary to determine continuously the present pitch angle of the deck.

To supply continuously information on the magnitude of the present ship pitch angle, service of a stable element is required. This stable element could be of any wellknown construction. For example, it could be one of the stable element-s commonly employed in connection with firing control systems in warships. The-re is also the possibility that the stabilizer unit required in connection with the radar antenna drive could also be used to supplyy continuously the present pitch angle.

Having determined a value for the prediction time Tp, the second phase of the prediction problem is entered into, namely the deck tilt Pp at the future time Tp. Consider first a ship at rest in still water. If now a moment should be applied about an athwartship axis through the center of gravity, some pitch angle, say P would result. Upon removal of this applied moment, the ship would oscillate in pitch about the athwartship axis with decreasing amplitude, the equation of. mot-ion being approximately where I is the effective ylongitudinal moment of inertia of the ship about the athwartship pitch axis, C is the damping moment coefiicient due to skin friction and the like, K is the hydraulic restoring moment coefficient, P is the second derivative of -the pitch angle, with respect to time and P is the first derivative of the pitch angle with respect to time. Now the period or this oscillation is the pitching period of the ship and is equal to Where wnp=natural angular frequency of pitch. However, when the ship is in a seaway, the equation of motion (18) becomes where F(t) represents the pitch component of the moment applied to vthe ship by wave action. Now from general observation, it can be said that F(t), although highly variable, will nevertheless at a given hour exhibit a frequency spectrum -in which certain narrow bands of -frequencies `are predominant. From an analyzed recording of pitch angle of various type ships headed into the Wind under different sea conditions over extended periods of time, it would =be possible to obtain the frequency spectrum of the ships pitching motion under the conditions existing at the time of the run. From this data, it would be noted 'that the frequencies of greatest amplitude would correspond to the natural pitch period of the ship, the periods at which the ship is encountering the particular Wave systems running at the time, the period of ship roll and the period of heave. The last two periods mentioned would probably be of small import and are included lonly because of the fact that both rolling and heaving cause an induced pitch. Usually, but not always, there will be .la single system lor" waves running. Furthermore, this system of Waves will more often than not be running in nearly the same direction :as the wind. Hence, the normal expectation during carrier landing operations is that the ship would be headed in a direction -about opposite to that in which the waves are traveling. Considering that the usual period or ocean waves is in the range of 5 to 10 seconds, a ship speed `of 25 knots would reduce these periods toi the range of 1.8 to 5.5 seconds. It .almost seems from theseconsiderations that under such conditions, the only period to be seriously considered in pitch motion would be the natural pitch period. That is, a forming moment function of 2 second period would have to be of tremendous magnitude to appreciably affect the ship motion in pitch. How-- ever, a forcing yfunction of 5 second period might Well have an appreciable effect, and of course la longer period forcing function would |have still greater iniiuence. Functions having such longer periods would arise if the normal conditions outlined above did not hold-as for example,` when the wind is opposite in direction to the sea and the ship is traveling with a following sea.

From the labove discussion, it is evident that 'an exact solution for the equation of motion of the ship is not possible. However, the equation of motion may be represented with suiiicient yaccuracy by the `approximation IP+KP=F(1) :a sin (wt-Hp) where FU) is a sine function of unknown amplitude a,

Q2 angular frequency w and phase angle qb. The solution of this differential equation is then of the form w1 and W2 being the unknown angular velocities and 1p1 and o2 the phase angles of the simple harmonic motions of which the pitch angle is assumed to be composed. This form, involving the six unknown parameters ai, a2, w1, W2, el and (p2 therefore represents the time variation-s of pitch angle. Hence, if these six unknown-s and Variable parameters can be continuously determined and furthermore if Aa continuous value of prediction time Tp is available, then the predicted pitch angle is Pp=al sin lll1(iTp)`i-1l "iz sin [Wzri-Tpl-l-Ml (21) The problem is now therefore reduced to the continuous determination of the six unknown and variable parameters noted above.`

The prediction method of the present invention is essentially based on establishing an oscillating system Whose diierential equation or" motion is from which we obtain by differentiation,

P50-H w12+w22h136+Wigwzgp=0 (36) Where p equals the differential operator as( l and 9 equals pitch angle in terms of angular displacement of shaft. Equations 85 and 86 when integrated will give the basic formula for an oscillating system ot" two simple harmonic components in the form raced d illustrated diagrammatically in FIG. 1 in which the full lines indicate shaft rotations. This rate measuring device comprises a comparison dilterential 3&5 into which are fed the quantity i corresponding to the present pitch angle obtained from the stable element 19, and the quantity 00 or 0 which is one of the outputs of the device, to obtain an error signal e equal to 01-00, this error signal being fed successively into a series of integrators 396, 397, 398, 399, 466 and #lill through successive stabilizing differentials 432, 493, 464, 405 and 406. By means of the arrangement described, there is obtained therefrom the output quantities p50, p40, p30, p26, p0 and 0, as shaft rotations, the latter quantity constituting the zero derivative value of 01 and being the same as H0.

ln connection with the rate measuring device of FIG. l described, it should be noted that pn@ is not exactly equal to pfi. An analysis of the deviations involved show how small and insignicant these deviations are.

9=e=.9,-e KrP=K1Pf9i-U1P+UE K1K2P20=K1K2P261 (KiKzPZ-l-KzP-r 1 e KllrgKgpgzKlKgKps (Kil-'ZKSPLlKzKaPz-FKSP 'l- 1 6 KIKZI3K4P42K1K2K3K4P@ (K1KzKsK4P4i-K2KaK4P2-l-K3K4P2-i-K4Pi-1 )e K1K2K3K4K5P59=K1K2K3K4K5P591 -(K1K2K3K4K5P5-l-K2K3K4K5P4 +KSK4K5P3 iK4K5P2+K5P -l- 1 e I 1K2K3K4K5K5I16=K1K2K3KllgKpGj (K1K2K3K4K5 KBPG+K2K3K4K5K6P5 *i- +K5KGPZ+KGPM= Here, the Ks are constants associated with the integrator given by the subscript. Thus, if the integrator output is p13-1gb, the input is Knpn.

Furthermore, from the last equation of the set above similar to Equation previously discussed. The Equations 85 and 86 are `derived from Equation 2Gb as follows:

(wlLl-WazlVZ-Ui(Wi-lWiZWzz) Sin (Wifi-$1) *512(W12W22-l-W24) Sil (unici-52) wl2w220=a1w12w22 sin (wlt-l-qbl) +a2w12wg2 sin (wzt-l-eg) By adding the quantities onthe left side of the equations and the quantities on the right side of the equations (the latter quantities cancelling out to zero), Equation 85 will result.

If at an arbitrary time t, We set the system oscillating with initial conditions given by the rates of the quantity 0, namely, at, pt, p2r9t, etc., and arrange the system so that Equation 85 necessarily holds, then the output of the system will be given by Equation 2Gb. Therefore, the predicted pitch angle t-TTD or 6p Will be given when the system has run for the interval TI, from vthe starting point with all initial conditions set. Here it should be noted that the mechanism time scale can be made much faster than the actual time scale, so that many 6p readings can be obtained. Thus we may obtain a series of discrete values of 6p by repeatedly resetting the oscillating system to new sets of initial conditions. The resulting values of Hp may be smoothed by Well known methods to obtain a continuous output.

The prediction system just described consists essentially of three mechanisms, namely (l) rate measuring device for determining the rates of the quantity d, i.e. Ot, p0t, pzt etc., (2) angular velocity function computer for determining w12w22 and will-w22 and (3) oscillating prediction mechanism for determining the value 6p from the quantities derived from the angular velocity function computer and the derivatives of 6,.

A mechanical form of rate measuring device 394 is Accordingly for aperiodic operation FIG. 2 is a diagram of a rate measuring device 3:94a which is an electrical equivalent of the mechanical rate measuring device 394 illustrated in FIG. 1, the solid lines in said diagram representing electric signals and specifically voltages proportional to the values of the quantities indicated. In this electric rate measuring device, there is provided an adding network 395e: which has an input the quantity 6i obtained from a stable element 10a and which corresponds to the comparison differential 395 of FIG. l, integrating networks 595g, 397e, 398er, 399:1, 40051 and lilla corresponding to the integrators 396, 397, 398, 399, 4Q@ and 401, respectively of FIG. 1, and stabilizing resistances or feed-back elements 402er, 40311, 404er, iilSa and 466:1 corresponding to the stabilizing differentials 492, 463, 404, 495 and lilo respectively of FIG. 1. The input 0i into the rate measuring device will be a voltage obtained by impressing the shaft rotation from the stable element as a slider movement upon a potentiometer, while a reference voltage is also impressed on the resistance of said potentiometer to obtain the output 0, as a voltage proportional to said shaft rotation.

The potentiometer for this purpose is described more fully in the aforesaid copending application. The voltage outputs of the electrical rate measuring device of FIG. 2 are p50, p40, p30, p20, p0 and 9.

FIG. 3 shows diagrammatically an angular velocity function computer 409 for obtaining the Values of wlzwzz and W124-w22, the solid lines indicating electric signals and specifically voltages and the dotted lines indicating shaft displacements. The inputs into this computer 409 are the outputs p50, p40, p30, p20, p6 and 0 of the rate measuring device of FIGS. 1 or 2. If the outputs from the mechanical device of FIG. 1 are employed, these must be converted into corresponding voltages before they can be used in the angular velocity function computer of FG. 3.

The computer of FIG. 3 is divided into two sections F and G. Section F mechanizes equation The computer 409 of FIG, 3 employs a stabilizing feedback. For that purpose, there is formed the auxiliary quantity:

The mechanism is designed so that the adjusting feedbacks are Referring to the angular vel-ocity function computer 469 of FIG. 3 and especially to its section F, the input 0 as a voltage is imposed on a potentiometer 410, having its slider adjusted by the mechanical output quantity w12w22 to produce an output voltage w12w220. This latter voltage, the input voltage p40, and the voltage obtained from a potentiometer 411 as will be described are fed into an adding network 412 to obtain an output voltage corresponding to the error e1 in Equation 85a. This vo1- age e1 is amplified and converted into a shaft rotation by a servo follow-up control system 413 of the type described in the aforesaid copending application. This shaft displacement 61 from the control system 413 is imposed upon a potentiometer 414 in conjunction with the input voltage to obtain an output Voltage equal to 2610. This voltage 2610 and the voltage 2e2p9 obtained from the output of a potentiometer 415 in a manner to be described are fed to an adding network 416 to obtain a voltage output equal to 2e10+2e2p0. This latter quantity is converted into a corresponding shaft displacement by means of a servo follow-up control system 417 similar to the control system 413 and to the control system described more fully in the aforesaid copending application. The output of this control system 417 is a shaft displacement corresponding to the quantity 26104-262110 which is equal t0 under the relationship (87) developed to obtain a stabilizing feedback. This partial differential is equal to l d(w12w22) k1 dt as indicated in the relationship (89) due to the selected design of the mechanism, and when this quantity is integrated in a unit 418, there results an output quantity w12w22 from the section F of the mechanism embodied in a shaft displacement.

The quantity W124-w22 is obtained from section G of the angular velocity function computer of FIG. 3 in a similar manner. For that purpose, the input p0 as a voltage is imposed on a potentiometer 420 having its slider adjusted by the mechanical output quantity w12w22 to produce an output voltage w12w22p9. This latter Voltage, the input voltage p50, and the voltage (w12.-{-w22)p30 obtained from a potentiometer 421 as will be described are fed into an adding network 422 to obtain an output voltage corresponding to the error e2 in Equation 86a. This voltage e2 is amplified and converted into a shaft displacement by a servo follow-up control system 423 similar to the unit 413. This shaft displacement e2 is imposed upon the potentiometer 415 in conjunction with the input voltage p0 to obtain the voltage quantity 2ezp0 for supply to the adding network 416 as described, and is also imposed upon' a potentiometer 424 in conjunction with the input voltage p30 to obtain an output voltage equal to 2e2p36'. An input voltage p20 and the mechanical error displacement e1 arerimposed upon a potentiometer 425, and the output voltage 2e1p20 from said potentiometer and the output voltage 2621236 from the potentiometer 424 are added in an adding network 426 to produce the voltage quantity 2e1p26+2e2p30- This latter quantity is converted into a corresponding shaft displacement by means of a servo follow-up control system 427 similar to the control system 413. The output of this control system 427 is a shaft displacement corresponding to the quantity 2e2p20-l-2e2p30 which is equal to under the relationship (88) developed to obtain a stabilizing feedback. This partial differential is equal to k2 as indicated in the relationship (90) due to the selected design of the mechanism, and when this quantity is integrated in a unit 428, there results an output quantity W124-w22 from the section G of the mechanism embodied in a shaft displacement. This quantity W124-W22 is fed into the potentiometer 411 in conjunction with the input voltage p20 to obtain the voltage quantity (w12-i-w22)p20 for supply to the adding network 412, and is also fed into the potentiometer 421 in conjunction with the input voltage p30 to obtain an output voltage corresponding to the quantity (w12-{-w22)p39 for supply to the adding network 422, as already described.

The quantities w12w22 and W124-w22 obtained as the mechanical outputs of the angular velocity function computer 469 of FIG. 3 are adapted to be employed in an oscillating prediction mechanism for determining the value 6p from these outputs.

FIG. 4 shows a mechanical oscillating prediction mechanisrn 439 adapted to apply to the mechanism as initial settings, at spaced time intervals during the predicted time period Tp of the run, the angular velocity functions obtained from the computer 499 (FG. 3) and the quantities 0, p0, p20, and p36 obtained from the rate measuring device 394 (FIG. l) and to be operated with said settings through oscillating cycles following the equational relationships and (86) but at a speeded time scale for Tp. From these oscillating cycles, a succession of predicted values for the pitch angle 0p at the predicted time Tp, to the speeded time scale, is obtained. These predicted values are close to the value 6p desired, and since the known initial conditions for the oscillating cycle are reset in the system for the successive cycles, the predictions become successively more accurate, as the predicted time Tp approaches zero. The predicted values therefore approach successively closer to the value of the desired pitch angle 6p.

In the diagram of the oscillating prediction mechanism 435 shown in FIG. 4, the solid lines indicate mechanical displacements and more specifically shaft rotations. This mechanism comprises in general four initial value resetting devices 44), 44l, 442 and 443, each adapted to store up mechanical quantities during each of a succession of cycles during a Tp run and to release or unload them after each cycle, so as to set up at the beginning of each integration cycle the quantities pH, p20, p3@ and p46 as initial values for integration through successive integrators 447, 446, 445 and 444 constituting part of the oscillating prediction mechanism 439. All of these devices 445, 441, 442 and 443 are similar in certain respects, so that devices 440 alone will be described.

The storing and unloading device 441') comprises a differential 450 with an input 6 which is one of the present or current mechanical outputs of the rate measuring device 394 (FG. l), another input which is designated as t?, indicating the pitch angle at a future time t, and an output equal to the difference between these inputs and connected to a heart cam 45t of the type well-known for storing and releasing rotational displacements at time intervals. Such heart cams are constructed in the wellknown manner, to cause the reaction of spring-pressed followers thereagainst, to displace in the absence of restraint the cams and the followers relatively into centered position with the followers in the valleys of the cams.

The heart cam 451 has a follower secured to a shalt 452 having a locking clutch connection 453 to a fixed frame 454 and carrying a heart cam 455. The follower of the heart cam 455 is connected to an element of a clutch 455 and to a heart cam 457 having its follower springpressed during certain phases towards the cam 457 and controlled by a solenoid 45S, The other element of the clutch 456 is rigidly connected by an unloading connector 460 to an input of a differential loi and is also connected to one element of another locking clutch 452, the other element of which is anchored to a iixed frame 463. The other input into the differential 461 comes from the output of the integrator 447 and the output from said differential is fed as an input into the differential 456.

In the operation of a storing and unloading cycle of the device 440, when a storing phase of said cycle is beginning, an integrating cycle with values initially set for integration as a result of a previous unloading phase is also just beginning. Under these conditions, the clutches and heart cams ot the device are in the positions shown in FIG. 4. During this initial storing phase, the input into the differential 458 will be 0, while the other input will be t, and the integrators 444, 445, 446 and 447 will have their timing discs just beginning to run. The output of the differential 459 will cause the heart cam 451 to rotate, and since the clutch 453 is open or disengaged, the follower of said heart cam will move with said cam and will move the heart cam 455 therewith. Ithe clutch 456 is disengaged, so that the follower of the heart cam 455 moves with said cam and the heart cam 457 is rotatively displaced in relation to its follower and without intreference therefrom, since the latter follower is withdrawn into inactive position away from said cam 457 by energization of the solenoid 458. The angular displacement of the heart cam 457 corresponds to the differences in the inputs into the differential 45d or tit-9:79p

During the storing phase described, the clutch 456 is disengaged and the clutch 452 is in engaged or locked position, so that the connector 46@ is locked against rotation. At the end of the storing interval, and at the end of the contemporaneous integrating cycle, the timing discs of the integrators 444, 445, 446 and 447 are shut-off, so that the integration cycle is ended and at the same time, or a short time thereafter, the clutches 453 and 456 are closed or engaged, the clutch 462 is unlocked or disengaged, and the solenoid 45S is deenergized or released, thereby causing the follower of the heart cam 457 to be spring-pressed against said cam, and said cam to be centered with respect to its follower. This causes the heart cam 457 to rotate to its original setting an amount which corresponds to the accumulated displacement thereof up to the period just prior to the shift in the conditions of the clutches 453, 456 and 462 and which is designated by the quantity Mt. With the clutch 456 now engaged and the clutch 462 unlocked, the return or unloading movement of the heart cam 457 is transmitted through the connector 466 to an input of the diterential 451 and this causes the output of said differential to rotate an amount equivalent to the input value 6 of the differential 450 just prior to the unloading cycle.

The mechanism is set up in assembly, so that the cams and the integrator carriages are in zero or centered position when the two inputs to each of the differentials 450 and the other corresponding differentials 465, 466 and 467 to be described are equal to zero. Under these conditions of assembly, during an integration period, while the value of the input into the dilerential 461 through the connector 460 is clamped or locked at a value Mt, the `output of the integrator 447 fed intot the other input of the differential 463i will be 19t-it, so that the output of the differential 45t fed into the dillerential 450 to Ht and at the end ot the speeded period Tp will be equal to one of the predicted values 6p to be sampled. When the displacement which has been storing up in the cam 457 is unloaded through the connector 466 into the differential 451 in the manner described, the output of the differential 45t by this unloading action will, because of the initial Zero setting at assembly, be equal to the input 0 of the di'erential 45t) just prior to said unloading action, as `already described.

The unloading movement ot the heart cam 457 moves the follower of the heart cam 455 relative to said heart cam 455, since said heart cam 455 is locked in position through clutch 453, While the follower of the heart cam 451 remains stationary, and the heart cam 451 is permitted to rotate.

As soon as the unloading is completed, the clutches 462, 456 and 453 are returned to the conditions shown in FIG. 4, and the solenoid 458 is energized to release the follower ot the heart cam 457 from the intluence of said cam. This operation restores the follower, of the heart cam 451 into centered position with respect to said cam, thereby causing the heart cam 455 to move into corresponding position, the follower of the heart cam 455 to be centered with respect to said cam, and the heart cam 457 to be moved into corresponding position. The device 446 is thereby set in the condition shown in FIG. 4 for the next storing and unloading cycle.

rthe storing and unloading devices 441, 442 and 443 operate in certain respects in a manner similar to the unit 449 described, with inputs p6, p20 and p30 from the rate measuring device 394 (FIG. 1) feeding into differentials 465, 466 and 467 respectively of said devices, correspending to the differential 45t) of the unit 440, to obtain the unloaded quantities Jpt, 11926, and Jpt. These unloaded quantities constitute changes in the values ofV pt, 11249, and p36, with respect tot the values p0, p28 and p30 respectively, just prior to the unloading operation, i.e. Jp=p0tpm JpzuzpZ-p@ and lptzgt-p. The storing and unloading devices 441, 442 and 443 include diiferentials 468, 469. and 470 respectively having one set of inputs arranged to receive the unloaded quantities ipe-, lpgt and Jpgat, having another set or inputs for receiving quantities from the output of preceding integrators and having outputs arrangedA to adjust theA carriages 

1. AN OSCILLATING PREDICTION APPARATUS FOR PREDICTING THE VALUE OP OF A FLUCTUATING SYSTEM AT THE END OF A FUTURE PREDETERMINED INTERVAL TP, WHICH COMPRISES MEANS FOR MEASURING THE RATES OF THE INITIAL OR PRESENT VALUES OF SAID SYSTEM, MEANS RESPONSIVE TO THE DETERMINATION OF SAID INITIAL RATES FOR DETERMINING THE INITIAL FUNCTIONS OF THE ANGULAR VELOCITIES OF THE SINE WAVE COMPONENTS OF SAID SYSTEM AT THE INITIAL OR PRESENT TIME, AND INTEGRATING 